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2.6 Inductive Transducer:
2.6.1 Linear Variable Differential Transformer (LVDT):
Passive inductive transducers require an external source of power.
The action of the transducer is principally one of modulating the excitation
signal. The differential transformer is a passive inductive transformer. It is
also known as the linear variable differential transformer (LVDT) and is
shown constructively in Fig. (2-19)(a). It consists basically of a primary
winding and two secondary windings, wound over a hollow tube and
positioned so that the primary is between two secondaries.
An iron core slides within the tube and therefore affects the magnetic
coupling between the primary and the two secondaries. When the core is in
the center, the voltage induced in the two secondaries is equal. When the
core is moved in one direction from center, the voltage induced in one
winding is increased and that in the other is decreased. Movement in the
opposite direction reverses this effect.
In the schematic diagram shown in Fig. (2-19) (b), the windings are
connected "series opposing." That is, the polarities of V1 and V2 oppose each
other as we trace through the circuit from terminal A to terminal B. Consequently, when the core is in the center so that V1 = V2, there is no voltage
output, V=0.
When the core is away from center toward S1, V1 is greater than V2
and the output voltage V will have the polarity of V1.
Fig (2-19) The linear Variable Differential Transformer
(a) Construction. (b) Schematic Diagram
When the core is away from center toward S2, V2 is greater than V1,
and the output will have the polarity of V2. That is, the output ac voltage
inverts as the core passes the center position. The farther the core moves
from center. the greater the difference in value between V1 and V2, and
consequently the greater the value of V0. Thus, the amplitude of V0 is a
function of the distance the core has moved and the polarity or phase
indicates which direction it has moved Fig. (2-20). If the core is attached to
a moving object, the LVDT output voltage can be a measure of the
position of the object. One advantage of the LVDT over the inductive
bridge-type transducer is that it produces a higher output voltage for small
changes in core position. Several commercial models that produce 50 to
300 mV/mm are available.
This means that a 1-mm displacement of the core can produce a
voltage output of 300 mV. LVDTs are available with ranges from as low
as ± 0.05 in to as high as ± 25 in., and they art sensitive enough to be used
to measure displacement of well below 0.001 it. They can be obtained for
operation at temperatures as low as -265°C and as high as +600°C, and
they are also available in radiation-resistance designs for operation in
nuclear reactors.
Fig (2-20) Output Voltage of LVDT
(a) Phase Relationship. (b) Absolute Magnitude
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Typical applications that illustrate the capabilities of LVDTs
include controls for jet engines in close proximity to exhaust gases and
measuring roll positions and the thickness of materials in hot-stripe or
hot-slab steel mills.
Example (7) An ac LVDT has the following data: input 6.3V, output 5.2V,
range ±0.50 in. Determine
(a) The plot of output voltage versus core position for a core
movement going from +0.45 to -0.03 in.
(b) The output voltage when the core is -0.25 in, from center.
(a) A core displacement of 0.5 in. produces 5.2 V. Therefore, a
Solution
0.45-in.
core movement produces
(0.45) (5.2)
 4.68V . Similarly , a  0.30  in
0.5
core movement produces
(0.3) (5.2)
  3.12V
 0.5
(b) A core movement of –0.25 produces
(0.25) (5.2)
  2.6V
 0.5
2.6.2 Theory of Operation of LVDT:
This is the most widely used inductive transducer for translating
the linear motion into an 'electrical signal. The basic construction of an
LVDT is shown in fig.(2-21).
Fig (2-21) LVDT
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LVDT is a differential transformer consisting of one primary
winding P and two identical secondary windings S1 and S2 wound over a
hollow bobbin of non-magnetic and insulating material. The secondary
windings S1 and S2, which have equal number of turns, are arranged
concentrically and placed either side of the primary winding P. A soft
iron core, attached to the sensing element of which displacement is to be
measured, in the shape of rod or cylinder slides freely in the hollow
portion of the bobbin. In order to overcome the problem of eddy current
losses in the core, nickel-iron alloy is used as core material and is slotted
longitudinally. Primary winding is connected to an ac source of voltage
varying from 5 to 25 V and of frequency ranging from 50 Hz to 20 kHz.
When the core is moved inside the bobbin it varies coupling of primary
winding to secondary windings S1 and S2. In null position of the core i.e.
in central position, coupling of primary winding to both of the secondary
windings are equal and so output voltages induced in secondary windings
S1 and S2 are equal. As the core is moved toward left from its null
position, the magnetic linkage to secondary winding S1 increases and to
secondary winding S2 decreases because the portion of the core inside
secondary winding S1 increases and that inside secondary winding S2
decreases. Therefore output voltage induced in secondary winding S1
increases where as the output voltage induced in the secondary winding
S2 decreases. The movement of the core to the right will have opposite
effect. Secondary windings S1 and S2 are connected in series opposition
so that difference of output voltages of secondary windings gives the
measurement of displacement.
Difference of output voltages of secondary windings gives the
amount of displacement following a linear law. In either direction of
movement of the core, difference of output voltages increases or
decreases giving the idea of direction of movement. With the movement
of the core in one direction away from the null position, the differential
output voltage- increases and it is in phase with the input voltage of
primary winding where as the movement of the core in other direction
from the null position causes again differential output voltage to increase
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but 180° out of phase with the input primary voltage. Now by measuring
the magnitude and comparing the phase of differential output voltage
with the input primary voltage, amount and direction of displacement of
core may be determined.
Curve for variation of differential output voltage with displacement
of core -for an LVDT is illustrated in fig(2-22). From this curve it is clear
that this characteristic of LVDT is linear for limited range of
displacement (say about 5 mm either side from the null position) and
beyond this range curve; starts flattening out at both ends.
Fig (2-22) Variation of Differential Output Volt Age
With Displacement for LVDT
In practice, output voltage is not zero at null position but some
residual voltage exists at output terminals. of LVDT but usually it .is less
than 1% of maximum value of output voltage in linear range. This
residual voltage may be either due to magnetic unbalance or due to
electrical unbalance. Presence of harmonics in input supply voltage or
harmonics produced in the output voltage because of saturation of iron
core also -contributes to residual voltage. Stray magnetic fields may also
be the cause for residual voltage, which may be overcome by using a
magnetic shield slotted longitudinally and fitted over the transducer.
In commercially available LVDTS normally range for displacement
varies from ± 0.01 mm to ± 25 mm.
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2.6.3 Merits, Demerits and Applications of LVDTS:
Merits:1. LVDT has infinite resolution as it gives stepless output and it has
got no mechanical element to change output in discrete steps. Nowa-days transducers are available with the resolution up to 1 micron.
2. LVDT has almost linear characteristic with in its prescribed range.
Linearity up to ± 0.25% can be achieved in commercially available
LVDTS.
3. LVDT has high sensitivity. It usually varies from 10 mV/mm to 40
V/mm.
4. Its output is very high which, even in some cases, eliminates the
need for amplification devices.
5. These devices consume very less power (less than 1 watt).
6. LVDT can be used on high frequencies up to 20 kHz.
So motion frequency can be as high as 2 kHz, which is very high
and efficient. So these devices have good frequency response.
7. Output impedance of LVDT remains constant which in case of
potentiometer varies with displacement.
8. Absence of sliding contact makes LVDT a more reliable device.
9. LVDT has very low hysteresis so a good repeatability can be
achieved with it.
10.LVDT is very rugged device in construction so it can tolerate
shock and vibration without any adverse effect.
11.It is a very stable and easy to align and maintain due to simplicity
of construction, small size and light weight.
Demerits:
1. These devices are sensitive to stray magnetic fields but its
problem is overcome by using magnetic shields.
2. Relatively large displacements are required for appreciable
differential output.
3. Sometimes, the transducer performance is affected by vibrations.
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4. The receiving instrument must be selected on ac signals or a
demodulator must be used if a do output is required.
5. The dynamic response is limited mechanically by the mass of the
core and electrically by the frequency of applied voltage. The
frequency of the carrier should be at feast 10 times the highest
frequency component to be measured.
6. Temperature affects the performance of the transducer. Manganin
wire may be used in place of copper wire to overcome the above
problem but due to high resistivity of manganin sensitivity is
reduced-may become as low as one-fifth of that with copper coils.
Temperature may also cause phase shifting' effects which may
be reduced to minimum using a capacitor across one of the
secondary windings.
2.6.4 Applications of LVDTS:
Are suitable for use in applications where the displacements are
too large for strain gauges to handle. For example, LVDTS can be
employed for measurement of displacements that range from a fraction of
a mm to a few cm. If LVDT is to be employed for measurement of
mechanical displacement greater-Than 25 mm, an appropriate mechanical
ratio (gearing) must be used.
Since the LVDTS can also be connected to other transducers
whose outputs are mechanical displacements these are often employed
together with other transducers for measurement of force, weight
pressure can be calculated as in eqn (11), (12).
S
RMSvalueofvoltage
Displaceme ntinm
(11)
Outputvoltage
LVDTsensit ivity
(12)
P
2.7 Photo-electric Pickup Tachometer:
Such a tachometer essentially consists of light source, a photocell
and a rotating disc placed between the light source and the photocell as
illustrated in fig. (2-23) the disc has a number of equidistant holes on its
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periphery and is mechanically coupled to the shaft of the machine whose
speed is to be measured. When the opaque portion of the disc is between
the light source and. the photocell, the latter does not get illuminated and
so does not give any output. But when a hole comes in between the light
source and photocell, the light falling upon the cell gives an output pulse.
Thus the photovoltaic cell is constantly turned on and off, at a frequency
which depends on the number of holes on the disc and its speed of
rotation (13) and (14).
Fig (2- 23) Photoelectric Pickup Tachometer
The frequency of the output pulses is given by the expressions (13)
and (14)
t = Speed in rpm x number of holes on the disc
or rotational speed in rpm =
6Cf
Number of holes on disc
(13)
(14)
As the number of holes in the disc is fixed and known so the
rotational speed can e determined simply by measuring . The pulse rate
with an electronic counter can be calibrated to indicate directly the
speed of rotation in rpm.
The advantages of such an arrangement are that it gives pulses of
constant amplitude and so needs simple electronic circuitry and gives
output in digital format and so does not require any A/D converter when
used in a digital instrumental system.
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